I am on my first major bike tour and am in the middle of nowhere in China, after 2 weeks of rain and mud, and have run out of chain lube. There is no bicycle shop which will stock syn lube or any other bicycle-specific lubricant for hundreds of miles. What else will work? (considered common vegetable oil but apparently this is bad...)

Any lubrication is better than none, even furniture "wax".
Thin oil will penetrate the inner parts of a chain but will soon need replenishing.
I have used standard engine oil on my MTB's but it soon gets black.